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Ellipse Tangents

Ellipse Tangents. How to find the point where a given focal ray intercepts an ellipse, and construct the tangent-line at that point. Finding the point-of-tangency. Given the angle a:. Construct point A so its distance from focus F 1 equals major-axis

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Ellipse Tangents

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  1. Ellipse Tangents How to find the point where a given focal ray intercepts an ellipse, and construct the tangent-line at that point

  2. Finding the point-of-tangency Given the angle a: Construct point A so its distance from focus F1 equals major-axis Construct the perpendicular bisector of the segment from A to F2 Point T is where that bisector meets the line-segment from A to F1 A T a axis F1 F2

  3. Proving the ‘Reflection Property’ Angle BTF1 equals angle CTA (these are “vertical angles”) Angle CTA equals angle CTF2 (angles in congruent triangles) Thus angle-of-incidence BTF1 equals angle-of-reflection CTF2 B A T C axis F1 F2

  4. Angle relationships Angle d equals one-half of angle g A T d g B d d a b a axis F1 F2

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